My research interests lie in symplectic/contact topology, algebraic/differential geometry, and mathematical physics.
More specifically, my current work investigates invariants of Lagrangian and Legendrian submanifolds arising from microlocal sheaf theory, with particular emphasis on their applications to diverse geometric and algebraic aspects of the study of Legendrian links. Looking ahead, I aim to explore connections between these invariants and those arising from Floer-theoretic constructions, as well as to work on the study of exact Lagrangian fillings and the categorification of braid varieties.
At the interface with mathematical physics, I am interested in the study of classical field theories within geometric, covariant Lagrangian and Hamiltonian frameworks, and in the understanding of several geometric and algebraic aspects of Deformation Quantization.
I am always open to discussing potential collaborations and new research directions.
A. Rodríguez–López, Computable sheaf invariants for Legendrian rainbow closures, arXiv:2511.15078 [math.SG], 2025, 156 pages.
J. Berra–Montiel, A. Molgado, and A. Rodríguez–López, A review on geometric formulations for classical field theory: the Bonzom-Livine model for gravity, Class. Quantum Grav. 38, 135012 (2021), arXiv:2101.08960 [gr-qc].
A. Molgado and A. Rodríguez–López, Covariant momentum map for non-Abelian topological BF field theory, Class. Quantum Grav. 36, 245003 (2019), arXiv:1907.01152 [gr-qc].
J. Berra–Montiel, A. Molgado, and A. Rodríguez–López, Polysymplectic formulation for BF gravity with Immirzi parameter, Class. Quantum Grav. 36, 115003 (2019), arXiv:1901.11532 [gr-qc].